The resistance per unit length is the cause of conductor loss in a transmission line.
Conductor loss, along with dielectric loss, is responsible for the signal attenuation in a transmission line.
The total resistance of a transmission line is the sum of the resistance of the signal trace and return path.
Printed circuit boards (PCBs) are indispensable parts of high-speed internet connections and fast ethernet buses. In these circuit boards, transmission lines are used to carry high speed and high bit-rate signals, and, ideally, they should be lossless. However, the vulnerability of transmission lines to signal reflections, crosstalk, and noise is so high that it poses a serious threat to signal integrity.
Irrespective of the type of transmission line, signals are impacted by losses due to the presence of line parameters, such as resistance (R), conductance (G), inductance (L), and capacitance (C), throughout the length and breadth of a circuit. The resistance per unit length is the cause of conductor loss in a transmission line. The conductor loss, along with dielectric loss, is responsible for the signal attenuation in the transmission line. In this article, we will discuss the details of conductor losses in transmission lines.
Resistance and Conductor Loss in Transmission Lines
Transmission lines are composed of two lines—signal trace and its return path. Typically, the return path is laid as a plane and the return current gets non-uniformly distributed over this plane. The current gets concentrated exactly beneath the signal trace in the return or ground plane. The return current takes up a strip of width three times greater than its signal trace above. The total resistance of a transmission line is the sum of the resistance of signal trace and return path, given by the following equation:
Considering the relationship between the geometry of the signal trace and return path mentioned above, we can write return path resistance as:
Equation (1) can be rewritten by substituting equation (2):
The resistance of the signal trace and return path offers resistance to the flow of current, and this is the cause of conductor loss in a transmission line.
The Dependency of Signal Frequency on Signal Trace Resistance
The current flow through a signal trace does not occupy the entire area of the trace. The depth of the trace occupied by the current flowing through it depends on the signal frequency. At low frequencies up to 1 MHz, the current flows through the entire trace, and the signal resistance can be given as:
As the frequency increases, the current starts to concentrate more on the surface of the trace or transmission line. This is due to a phenomenon called the skin effect in transmission lines. The effective area of the conductor is reduced due to skin effect and this increases the conductor resistance.
As the conductor resistance increases, conductor losses also increase. The skin effect is more predominant in traces carrying alternating signals of high frequencies. Incorporating skin effect into equation (4), T is replaced by 2ẟ, where ẟ is the skin depth of the trace where the current concentrates. The current utilizes the entire periphery of the transmission line conductor, therefore, 2ẟ is included in equation (5):
Signal Attenuation Loss
In transmission lines, signal attenuation is viewed as a problem affecting signal integrity, transmission reliability, and efficiency. In high-frequency communication lines or high-bit data rate transmission lines, such as ethernet bus circuits, signal attenuation can become severe, resulting in corrupt data.
Signal attenuation is mainly the effect of conductor losses and dielectric losses in a transmission line. Conductor losses are dependent on trace material resistivity and trace geometry. The conductance of the dielectric material between the signal trace and the return path is responsible for producing the dielectric loss.
The Conductor-Dielectric Interface
The conductor loss in a transmission line is also influenced by the conductor-dielectric interface. Usually, the conductor surfaces are kept rough where it interfaces the dielectric. The roughened surface attaches firmly to the dielectric and there is less probability of trace peeling off from the dielectric. However, the uneven conductor in the conductor-dielectric interface acts as a catalyst, which further increases the conductor loss and signal attenuation.
Calculating Signal Attenuation Loss
The signal attenuation loss of a transmission line can be given by equation (6), which is also called total insertion loss per unit length of the transmission line (𝛼t).
The term R/Z0 corresponds to conductor loss and GZ0 corresponds to the dielectric loss, where R, G, and Z0 are resistance, conductance, and characteristic impedance of the transmission line per unit length, respectively.
Using Trace Material as a Solution For Conductor Loss in a Transmission Line
Using trace material of high conductivity is one solution to overcome conductor loss in a transmission line. Modifying the trace length and width is also effective in reducing conductor loss. However, practical difficulties may arise with this geometry design modification. The amplitudes of currents, electromagnetic interference (EMI), and radio frequency interference (RFI) are some things that limit the modification of the trace geometry.
The signal integrity and reliability of a high-speed or high-bit data rate circuit are fairly dependent on the conductor loss in a transmission line. Cadence’s software can support the design of transmission line geometry to reduce conductor loss and dielectric loss.